few_shots: Example:
Problem/activity:
Task
Cruz and Erica were both getting ready for soccer.
Cruz ran 1 lap around the school.
Erica ran 3 laps around the playground.
Erica said,
I ran more laps, so I ran farther.
Cruz said,
4 laps around the school is 1 mile, but it takes 12 laps around the playground to go 1 mile. My laps are much longer, so I ran farther.
Who is right? Draw a picture to help you explain your answer.


Standard options: 
A. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
B. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.


Thought: This task asks students to compare two fractions that are equal. The two fractions have different numerators and denominators (e.g. 1/4 and 3/12). The students need to explain why the two fractions are equal by drawing a picture, which involves using visual fraction models.
Answer: A, B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: im_task_000212

4
options: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
problem_activity: Narrative
In this activity, students see that they can find equivalent fractions by dividing the numerator and denominator by a common factor. They connect this strategy to the process of grouping unit fractions on a number line into larger equal-size parts. The result is a fewer number of parts, and smaller numbers for the numerator and denominator of equivalent fractions.
MLR8 Discussion Supports.
Synthesis: At the appropriate time, give students 2–3 minutes to make sure that everyone in their group can explain the strategies used in the given examples. Invite groups to rehearse what they will say when they share with the whole class.
Advances: Speaking, Conversing, Representing
Launch
Groups of 2
Activity
“Work with your partner to answer the first three problems.”
“Be prepared to explain how you think Andre’s and Kiran’s strategies are related.”
7–8 minutes: partner work time
“Take a few minutes to answer the last problem independently.”
2–3 minutes: independent work time for the last problem
Student Facing
Andre drew a number line and marked a point on it. Label the point with the fraction it represents.
[IMG]
To find other fractions that the point represents, Andre made copies of the number line. He drew darker marks on some of the existing tick marks.
Label the darker tick marks Andre made on each number line.
[IMG]
[IMG]
Kiran wrote the same fractions for the points but used a different strategy, as shown. Analyze his reasoning.
\(\frac{8 \ \div \ 4}{12 \ \div \ 4}=\frac{2}{3}\)
\(\frac{8 \ \div \ 2}{12 \ \div \ 2}=\frac{4}{6}\)
How do you think Andre’s and Kiran’s strategies are related?
Try using Kiran’s strategy to find one or more fractions that are equivalent to
\(\frac{10}{12}\)
and
\(\frac{18}{12}\)
.
Student Response
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Activity Synthesis
“What did Andre do with the number lines? How would it help him find equivalent fractions?” (Andre grouped the 12 parts into equal groups of different sizes—2s, 4s—to make bigger parts. Then, he counted the number of those new parts.)
“What did Kiran do? How is his strategy related to Andre’s?” (Kiran divided 12 by 4 and then by 2, similar to how Andre put 12 parts into groups of 4 and then of 2.)
“Notice that the equivalent fractions
\(\frac{2}{3}\)
and
\(\frac{4}{6}\)
both have smaller numbers for the numerator and denominator than the original fraction. Can you use Andre’s number line to show why this might be?” (The size of the parts are bigger, so there are fewer parts in 1 whole.)
If time permits, ask students:
“How many equivalent fractions can you find for
\(\frac{10}{12}\)
using Kiran’s way?” (One) “How many can you find for
\(\frac{18}{12}\)
?” (Three)
“What might be a reason that you could find more equivalent fractions for
\(\frac{18}{12}\)
than for
\(\frac{10}{12}\)
?” (18 and 12 have more factors in common than 10 and 12.)
“How would you show
\(\frac{9 \ \div \ 3}{12 \ \div \ 3}=\frac{3}{4}\)
on the number line?” (Put the original 12 parts into groups of 3 to get 4 parts, each being a fourth. Mark 3 of those 4 parts to show
\(\frac{3}{4}\)
.)


correct_option_index: 1